A101128 - OEIS

%I #12 Jan 17 2019 13:44:06

%S 0,1,2,3,4,7,8,44,135,141,157,242,922,1234,2195,4649,6118,7323,9542,

%T 13493,20309,20359,232919,830864,902707

%N Indices of primes in sequence defined by A(0) = 71, A(n) = 10*A(n-1) - 9 for n > 0.

%C Numbers n such that 70*10^n + 1 is prime.

%C Numbers n such that digit 7 followed by n >= 0 occurrences of digit 0 followed by digit 1 is prime.

%C Numbers corresponding to terms <= 922 are certified primes.

%D Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/70001.htm#prime">Prime numbers of the form 700...001</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = A056804(n) - 1.

%e 700001 is prime, hence 4 is a term.

%o (PARI) a=71;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-9)

%o (PARI) for(n=0,1500,if(isprime(70*10^n+1),print1(n,",")))

%Y Cf. A000533, A002275, A056804.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(21)-a(25) from Kamada data by _Ray Chandler_, Apr 29 2015